The Loop is a concept discovered by Noctae which "sent owl society into infighting and chaos", creating social unrest and civil wars between the owls. It is not revealed what exactly The Loop is, leading to a lot of speculation and theories. It can be parsed that it has something to do with time or history repeating itself. This theory is supported by Noctae's hologram's statements about his use of math to predict events and how his calculations predicted his death repeating infinite times, like it was an "eternal wave function".
The Ancient Owls, specifically Noctae and Aegolius, created the Hex Machine to stop The Loop, but the machine failed, causing all of the landmasses on the planet to float into the sky, leaving the planet itself an empty ocean.
Not all owls believed in The Loop, at least at the beginning. In the Eternal Sanctuary the hologram of an owl similar to Asio (probably his ancestor) was skeptic about his theory, considering it not provable, although he admitted most of the owls believed in it.
It is unknown if the Hex Machine or the Anti-Hex had any effect on The Loop. Noctae's hologram pointed out his predictions about Otis' fate contradicted his other prediction of Otus watching his recording. He wondered if that inconsistency might mean his Hex Machine worked.